Today, non-energy use (e.g. production of plastics or fertilizers) represents about 10% of the final energy consumed worldwide and is dominated by petroleum products, natural gas and coal. However, due to complex flows of materials and ambiguities between net and gross energy in non-energy data sets, this sector is generally misunderstood. The defossilisation of this sector requires to properly define the lever of actions: can we use renewable alternatives to the currently used fossil fuels as direct inputs to this sector? Can the use of these alternatives in the non-energy demand be more efficient and lead to synergies with the other energy sectors (i.e. electricity, heat and mobility)? This paper focuses on the case-study of Belgium and its non-energy demand, mostly from chemical and petrochemical industries (20% of Belgium final energy consumption). It investigates the required molecules of the end-use demand, i.e. High-Value Chemicals (HVC), methanol, and ammonia, as well as the related mature conversion technologies. A transition is analysed to switch the production of the final molecules from fossil fuels to renewable resources as feedstock (e.g. HVC from naphtha-cracking to biomass gasification or methanol-to-olefins). To fully assess the role of these energy carriers, we used and customised Energy Scope TD, a whole-energy system model which optimises the design and hourly operation of an energy system to minimise its costs and emissions. With the aim of carbon-neutrality, this work emphasises the major role of biomass and methanol as the cornerstones to defossilise the non-energy demand, mostly for HVC. To do so, when reaching high global warming potential reductions, biomass is preferably converted into methanol and, subsequently, into HVC. Finally, given the limited availability of local renewables in Belgium, this study highlights the predominant impact of imports like ammonia and methanol.